Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

From MEMS to NEMS: Closed-loop actuation of resonant beams beyond the critical Duffing amplitude

Abstract: Because of its moderate cost in terms of electronics, resonant sensing has become commonplace in the context of MEMS and NEMS devices. It is usual to drive such resonators below the critical open-loop Duffing amplitude, above which the oscillations become unstable. However, when scaling sensors down to NEMS, nonlinearities may occur at very low amplitudes, making oscillations very difficult to detect. This paper describes a very general way to compute the critical amplitude in open-loop operation for beam resonators, before it focuses on closed-loop Duffing-type resonators. The major contribution of this paper is the use of describing function analysis validated by numerical simulations to show that it is possible to obtain stable oscillations with amplitudes much larger than the critical Duffing amplitude. As a practical consequence, the measured currents are significantly increased and the constraints on the sensing electronics can be relaxed.

Analysis of pilot-in-the-loop oscillations due to position and rate saturations

Abstract: In this paper we deal with the analysis of category II (nonlinear) pilot-in-the-loop oscillations (PIO). PIO phenomena are originated by a misadaptation between the pilot and the aircraft that causes sustained or uncontrollable oscillations, which especially occur during some tasks where tight closed loop control of the aircraft is required from the pilot. Category II PIO are those oscillations that can strictly be correlated with the activation of rate and position limiter elements in the closed loop pilot-vehicle system. This kind of nonlinearity is unavoidably present in every aircraft, because of physical constraints of elements such as stick/column deflections, actuator position and rate limiters, limiters in the controller software and so on. In this paper we propose an approach, based on the describing function technique, to evaluate the nonlinear effects of the simultaneous presence of position and rate saturations in the control loop. The X-15 landing flare PIO is used as test case to demonstrate the effectiveness of the method.

Parameter tuning and chattering adjustment of Super-Twisting sliding mode control system for linear plants

Abstract: A simple procedure for tuning the parameters of the Super-Twisting (STW) second-order sliding mode control (2-SMC) algorithm, used for the feedback control of uncertain linear plants, is presented. When the plant relative degree is higher than one, it is known [10] that a self-sustained periodic oscillation takes place in the feedback system. The purpose of the present work is that of illustrating a systematic procedure for control tuning based on Describing Function (DF) approach guaranteeing pre-specified frequency and magnitude of the resulting oscillation. The knowledge of the plant's Harmonic Response (magnitude and phase) at the desired chattering frequency is the only required prior information. By means of a simulation example, we show the effectiveness of the proposed procedure.

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

Abstract: This work deals with Single-Input-Single-Output (SISO) fractional order systems with a discontinuous relay control element in the feedback loop. Stable self-sustained oscillations often occur in the closed loop relay system, and this work takes advantage of Describing Function (DF) analysis and of another more accurate approach, called Locus of a Perturbed Relay System (LPRS) method, for analyzing in the frequency domain the characteristics of the limit cycle oscillations. The use of fractional lead compensator is also suggested for the purpose of shaping the characteristics of the limit cycle. The proposed analysis and design procedures will be supported by thoroughly discussed simulation examples.